Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
12,303 documents
The document explores how to set asset-level risk contribution budgets while also requiring a portfolio to meet a target volatility. It presents an optimization that minimizes squared differences between each asset’s share of portfolio variance and its…
The discussion distinguishes forecasting the variance of returns from forecasting their expected direction. A conventional GARCH model updates conditional variance using past squared residuals and earlier variance estimates, making it a framework for…
The document asks how to simulate paths for a mean-reverting diffusion without stepping through its stochastic differential equation directly. It gives the process solution over an interval and its conditional mean and variance, which together specify the…
The document asks how to value a one-year at-the-money European call when volatility is specified as 20% for the first half-year and 90% for the second half-year. The proposed answer combines the two periods’ variances, weighted by their durations, and takes…
The document explains how to interpret RiskMetrics decay factors in an exponentially weighted moving average volatility model. It uses the half-life formula to connect decay to the time required for an observation’s weight to halve, and describes why a daily…
The document asks how to estimate a portfolio volatility measure at a fixed time in Berlin when the portfolio spans US, European, and Japanese equity indices trading in different time zones. It considers using observations aligned to that local time and asks…
The document explores whether implied volatility in a diffusion model must be bounded by the model’s instantaneous volatility. It assumes the asset follows a stochastic-volatility diffusion under the pricing measure and considers a setting where…
The document asks whether a Heston stochastic volatility model and a local volatility model derived from it produce identical option prices. It points to a comparison in Gatheral’s book and asks whether the equivalence depends on spot and variance having…
The document examines how the sampling interval used to construct realized volatility relates to the estimated fractional differencing parameter d in an ARFIMA(0,d,0) model fitted to log realized volatility. The author reports that d appears to fall as bar…
The document explains calibration in the context of using the SABR stochastic volatility model to price foreign exchange call options. Calibration means choosing model parameters so that model outputs match observed market quotes as closely as possible. The…
The document addresses noisy volatility estimates for a market-making bot that receives frequent prices and maintains a rolling window of several minutes. It recommends estimating variability from tick-to-tick price changes or returns, rather than from the…
Dispersion has a broad statistical meaning: the spread of a distribution around its central tendency. Variance is a common measure of that spread, and standard deviation is its square root. In finance, volatility usually refers to standard deviation as a…
The document asks why the variance accumulated by a geometric Brownian motion over a time horizon is represented by the integral of instantaneous variance, and how time averaging enters the stated realized-variance expression. The answer builds the result…
The document addresses how traders can identify economic announcements that move different markets, with a particular question about agricultural commodities. It cites a study examining the immediate responses of commodity prices and short-term Treasury bill…
The document asks how to price American options when the underlying follows risk-neutral dynamics with volatility that varies with spot. The response identifies this as a special case of a local volatility model, where volatility may depend on time and spot,…
The document asks whether an equity’s implied volatility skew can reveal the probability of an equity move conditional on a change in implied volatility. It defines skew as the difference between implied volatilities at two option deltas and explains why…
The document compares two ways to summarize an asset’s historical return and volatility. One method averages daily log returns and scales the mean and standard deviation to an annual horizon; the other calculates each calendar year’s simple return and then…
The discussion addresses why a Carr–Madan fast Fourier transform calculation can return complex-valued quantities when pricing caplets. The accepted answer says the complex form is expected in the method and that the option price is obtained from the real…
The response points to an intuitive route to understanding Gyöngy’s theorem through European call prices and generalized derivatives. It starts from an asset whose drift follows a risk-neutral specification and whose volatility may depend on the adapted…
The question concerns how to infer an equity’s local volatility when its drift is the short rate and that rate is stochastic. The author proposes adjusting market implied volatility on a forward for short-rate volatility, then asks whether cumulative…
The document explains GSR as the Gaussian Short Rate model and gives its risk-neutral short-rate dynamics in mean-reverting form, with time-varying reversion, level, and volatility. It places GSR within the broader family of affine short-rate models, whose…
The document considers how to value currency options when a central bank caps an exchange rate, using the Swiss National Bank’s franc ceiling against the euro as context. Its answer argues that standard models calibrated to historical market behavior may be…
The document offers an intuitive explanation for why standard call and put options have positive gamma in the Black–Scholes setting. As the underlying price rises, a call’s delta rises toward one because the option behaves more like the underlying. A put’s…
The post asks whether linear interpolation of implied volatility can create arbitrage, distinguishing interpolation across maturities from interpolation across strikes. It notes the concern that interpolating volatility over time may violate calendar…